The Underground Experimental Investigation of Thermocouples April 14, 21 Abstract This experiment investigates a K-type thermocouple in order to demonstrate the Seebeck and Peltier coefficients. Temperature dependency of voltage and vice-versa are characterized for this thermocouple. A homemade thermocouple is built to find current, which is found as 4.1 ±.5 ma with junctions in liquid nitrogen and at room temperature, and 196.8 ±.6 ma for junctions in liquid nitrogen and being heated by a blow torch. Contents 1 Introduction 1 1 Introduction A single thermocouple is a junction between two dissimilar metals, with each metal at a different temperature. Due to the temperature difference between them, the two metals will induce an electric current running along the wires connecting them [2]. Hooking up a voltmeter to the circuit allows the voltage across the circuit to be measured. Each thermocouple usually produces a voltage on the order of 1-5 microvolts. A system of thermocouples connected in series is called a thermopile. Such circuits have interesting consequences, and two of those will be investigated in this experiment. 2 Theory 1 2.1 Part I: Seebeck Effect........ 1 2.2 Part II: Peltier Effect......... 2 2.3 Part III: Build-a-thermo....... 2 3 Experimental Methods 3 3.1 General Calibration......... 3 3.2 Part I: Seebeck Effect........ 3 3.3 Part II: Peltier Effect......... 4 3.4 Part III: Build-a-Thermo...... 5 4 Results and Discussions 5 4.1 Part I: Seebeck Effect........ 5 4.2 Part II: Peltier Effect......... 7 4.3 Part III: Build-a-Thermo...... 7 5 Conclusions 8 6 Acknowledgements 8 2 Theory 2.1 Part I: Seebeck Effect The Seebeck effect, named after Estonian-German physicist Thomas Johann Seebeck, deals with the voltage potential resulting in connecting two dissimilar metals at two different temperatures. 1
difference, and using regression to find the coefficients for the polynomial fit. 2.2 Part II: Peltier Effect Figure 1: Schematic Diagram for a Seebeck Circuit As shown schematically in figure 1, by taking two different metals (A and B) at different temperatures (measured at T1 and T2) one can produce a voltage across the circuit. The equation to find voltage as a function of temperature is: V S = T2 T 1 (S B (T ) S A (T )) dt (1) Figure 2: Seebeck s Equation In this case, S A (T ) and S B (T ) are the Seebeck Coefficients as functions of temperature. If over the range of temperatures tested the coefficients can be considered constant, the equation can be reduced to: V S = (S B S A ) T The method used by Seebeck himself to find the coefficients was: [3] S = Figure 3: Calculation of the Seebeck Coefficient V T (2) For the purposes of this experiment, it would be very difficult to calculate the Seebeck coefficients from pure theory. Therefore, we are simply satisfied by finding voltage as a function of temperature The French physicist Jean-Charles-Athanase Peltier discovered the effect that is now named after him, the Peltier Effect. Peltier discovered that given two connected dissimilar metals, applying a voltage potential to the circuit will result in a temperature difference at the input and output connections of the metals [4]. Although Peltier makes use of the same setup as Seebeck (see figure 1), this is the reverse of the Seebeck effect, in the sense that instead of measuring a voltage difference, one is applying a voltage difference and in turn measuring the temperature gradient resulting from it. Q = Π AB I = (Π B Π A ) I (3) Figure 4: Peltier s Equation In the equation above, Q represents the amount of heat absorbed by the lower junction (labeled T2 in figure 1) per unit time. Π AB is the Peltier Coefficient for the entire system, which can be calculated from Π A and Π B, the corresponding Peltier Coefficients from metals A and B. Although the Peltier coefficients themselves can be quite hard to find, there is a way to calculate them using the corresponding Seebeck coefficients [3][4]: Π = (S A S B ) T (4) Figure 5: Calculation of the Peltier Coefficient In this equation, the S A and S B correspond to the materials A and B respectively. Just like in Part I, the calculation of the Peltier coefficients is very theoretically rigorous, so finding the temperature difference as a function of voltage applied will suffice for this experiment. 2.3 Part III: Build-a-thermo Here we build our own thermocouple. This part of the project basically involves the first part, but on 2
a much larger scale. Instead of applying a heat difference on the ends of wires, we built a much larger circuit (and used aluminium and copper instead of alumel and chromel alloys). The purpose of this was to be able to generate a stronger current than with the wires. Due to the large cross section area between the different metals in the larger circuit, it is theoretically possible to pass more current. Amplified Voltage (V) 2 15 1 5 y = 82.164*x.25233 Data Linear Fit 5 3 Experimental Methods 3.1 General Calibration 1 15.8.6.4.2.2.4.6.8 Input Voltage (V) Due to the fact that thermocouples the size that we were using usually generate a maximum voltage of about 4 mv [1], we decided that the thermocouple should be sent through an amplifier before letting the Labmaster record the voltage. Since the changes in voltage were too minute for the Labmaster to distinguish, it would either round up or round down the voltage to the nearest bit. For this reason we built our own amplifier. In order to construct our own op amp, we followed the following design: Figure 7: Amplified voltage versus applied voltage Using simple linear regression, we found the slope of the linear fit, and therefore our actual gain, to be (82.19±.4). Looking at the residual plot below, one can see that the slope of the linear fit indeed is the actual gain on the amplifier..15 Residuals.1 Magnitude of Residual (V).5.5 Figure 6: Schematic diagram for an op amp.1.2.15.1.5.5.1.15 Input Voltage (V) Figure 8: Residual plot for the amplification factor The values of the resistors used were 1kΩ for R1 and 82kΩ for R2. This means that our total gain was (theoretically) x82. In order to obtain the actual amplification of the voltage, we applied a certain voltage using the DAC, ran it through the amplifier, then measured the voltage using the ADC. The following plot was obtained: 3.2 Part I: Seebeck Effect The first part of this experiment involves applying heat to one side of the thermocouple, and registering the voltage potential across the circuit. This is 3
called the Seebeck Effect. In order to measure this effect, we first had to calibrate the zero-point of the thermocouple. For that, we put both junctions of the thermocouple in an ice-water bath, in order to maintain both ends of the thermocouple at the same temperature ( C). Theoretically we should have registered an amplified voltage of V, since there was no heat difference between the two ends. However, due to systematic errors, we registered a constant voltage of.27 V. This means that when both ends of the thermocouple are at the same temperature, there is an unamplified voltage of 3.3 mv across the circuit. This offset was accounted for during the rest of the experiment. A schematic diagram for this part of the experiment is provided: 3.3 Part II: Peltier Effect Figure 1: Schematic diagram for the Peltier Effect Figure 9: Schematic diagram of Seebeck Effect As is evident form the diagram, one end of the thermocouple was heated in the heater, and the other end was dipped in liquid nitrogen. The voltage that developed across the thermocouple was then sent through an amplifier. This voltage was then recorded and analyzed. As can be seen by the schematic diagram (figure 1), finding the setup to measure temperature difference as a function of voltage applied proved to be tricky. Since it was not possible to measure temperature directly while applying a specific power to the circuit, the results from Part I (where voltage as a function of temperature was found) were used to find the temperature of the thermocouple at any specific temperature. Therefore, the purpose of the switch was to allow the collection of data as fast as possible; in this case the voltage that developed across the thermocouple as soon as power was no longer applied to the circuit was recorded. In figure 1, the thermocouple (connected in the middle of the switch) was not connected to anything other than the two circuits to the left and right of it, depending on where the switch was located. One end of the thermocouple was in liquid nitrogen, and the other was at room temperature. When the switch was connected to the circuit on the left, all it was doing was applying a voltage (in essence a certain power) to the thermocouple, causing a temperature difference at the junctions. Then, the switch was 4
shifted to it s position on the right, where the data collection occurred. At the moment the switch is shifted to the position on the right, it can be assumed that any voltage across the thermocouple is entirely due to the fact that the junctions are at different temperatures, since the circuit on the left is open. This voltage was then run through an amplifier and recorded. 3.4 Part III: Build-a-Thermo A schematic diagram for this part of the experiment is given below: A large deal of calibration is involved in order to be able to accurately describe the thermocouple properties. We can use known temperatures to find accurate measurements of potential difference for the thermocouple used. These temperatures include a C point for an ice bath, a 24.5 C point for the room temperature and finally, 1 C for boiling water. To test these three potential differences, we leave one junction of the thermocouple at room temperature whereas the other is either placed in an ice bath or in boiling water. The graph below describes these three points, and their approximately linear relationship..3.25 y =.3288*x +.5459.2 Potential Difference (V).15.1.5.5 data linear fit.1.15 4 2 2 4 6 8 Temperature Difference ( C) Figure 11: Schematic diagram of the hand-built thermocouple Since there are large plates of aluminium and copper attached to each other, more of a current can pass through a large surface area, as opposed to wire. Here, we attach a plate of aluminium to a piece of copper, and dip that part into liquid nitrogen. The other junction is left exposed at roomtemperature. To find the magnitude of the current going through, an ammeter is used. 4 Results and Discussions 4.1 Part I: Seebeck Effect Figure 12: Plot and linear relationship describing a K-type thermocouple at low temperature differences In reviewing this section, it is possible to assume a linear relationship between potential and temperature because the coefficients of larger degrees of x are very small. The values for each temperature difference are found by finding the mean potential over 3 seconds for the three given scenarios. Thus, there is an error associated to each measurement, which is on the order of 6.983 1 4, so it is barely visible on the graph. In terms of performing the actual experiment, it is possible to find the power applied that is associated to a certain known temperature, and can therefore use this point as a reference point for P max. One that suits particularly for this experiment is the melting point of lead, which is known to be 327.46 C, so a small block of lead is placed in 5
an opening of the heated aluminum block. We can visually and physically find at which potential the lead piece begins to melt, cool the block down then heat it up again and once again note the potential at which it melts. An average of the two potentials therefore provides us with the input power needed for the rest of the experiment. The graph below notes the potential as a function of temperature as the block of aluminum is heated. Amplified Output Potential (V).9.8.7.6.5.4.3.2.1 Amplified Output Voltage (mv) 14 12 1 8 6 4 2 2 5 1 15 2 25 Figure 13: Plot describing a block of aluminum being heated up to produce a potential difference 5 1 15 2 25 3 35 Figure 14: Potential from thermocouple when 12.8 W of power are applied Finally, in order to fully understand the Seebeck effect, we heat up a block to reach the point where the power differential is no longer a function of time, so the potential will become constant at a large enough temperature. Unfortunately, in this experiment, the wires used for the thermocouple and the heater were not exactly the highest grade, so were unable to take such high values of power. This resulted in a short circuit, which is viewable after about 13 seconds on the graph below. 1.6 1.4 The potential difference, from the graph is found to be 1173.6 mv (the mean of the two peaks) with a temperature difference of 32.96 C. The power associated with this voltage, which will serve as P max for other experiments, is.1796 W, after most of the applied power is dissipated. Amplified Output Voltage (V) 1.2 1.8.6.4.2 By applying different levels of power to the block, and seeing the potential response the thermocouple achieves, we can find the energy that is lost to the environment and approximate a value of Q, the heat flow of the aluminum block. One such result is displayed below and there are similar results for other values of power..2 5 1 15 Figure 15: Plot describing a potential function as an aluminum block reaches a certain temperature Due to this unfortunate occurrence, we were unable to calculate the coefficients for the data ob- 6
tained, but can confidently say that the technique is appropriate enough for better experimentation methods. It would be possible to find much more precise ways of containing the power associated with heating up the block and to have much lower levels of power dissipated, but would be more expensive and would demonstrate the same overall effects as in those above. This fit would also have aided to describe the next section, since we would have determined a voltage-temperature correlation accurately. By characterizing the temperature dependency, the Seebeck coefficients could have been used in a way to find the temperature change between the two junctions in the following section. 4.2 Part II: Peltier Effect The Peltier effect is seen to be a reversal of the Seebeck effect, since we are now applying a potential across the thermocouple and measuring the temperature difference. By applying a large enough power, the potential at the junctions will exhibit different values, therefore satisfying a difference in temperature. By comprising a switch as described in the experimental methods, we are able to do so while simultaneously collecting data for this occurrence. The graph below describes the potential as soon as the power is shut off, and the measurement of the potential at two junctions is found. From the graph, we can see that the base potential is around 532 mv, which is such because the thermocouple is placed with one end in liquid nitrogen and the other at room temperature, so there is not as much variation in the measurements. Also, the power applied for this experiment is on the order of 19 W, which is quite difficult for such small thermocouple wires to handle. When measured, the power dissipated in the wires to the environment accounts for more than 8% of the applied power. The overall potential however, is still a function of this smaller element of power and exhibits the properties as shown in the graph. 4.3 Part III: Build-a-Thermo There are two formats we took to building our own thermocouple, one was with one junction in liquid nitrogen with the other at room temperature, whereas in the other format, one junction was in liquid nitrogen and the other was heated with a blowtorch. It is assumed that a larger potential would be found when one junction is being heated as compared to where one is left at room temperature. The data from the first format is presented below..5.49 1.3 1.2 1.1 Amplified Output Voltage (V).48.47.46 Amplified Potential (V) 1.9.8.45.44 1 2 3 4 5 6.7.6.5 2 4 6 8 1 12 14 16 Figure 16: Plot of the potential difference between two junctions after power applied goes to W Figure 17: Potential measured with one junction at room temperature and the other in liquid nitrogen with a thermocouple The data is obviously quantized, between two successive values, so the actual potential measurement is somewhere between the two, and taking 7
the mean, we find 48.1 ±.2 mv. The resistance is measured as 1.2 ±.1 Ω, so the total current is 4.1 ±.5 ma. This is an interesting result obtained, since there is no real isolation of the metals. For the second format, a blowtorch is used as a way of heating the external junction, and the results are shown in the graph below. results from that section are much clearer and welldefined. In building our own thermocouple, we were able to find the current flowing through the junctions as being 4.1 ±.5 ma and 196.8 ±.6 ma for the liquid nitrogen/room temperature configuration and liquid nitrogen/blow torch configuration, respectively. Output Voltage (V).1.9.8.7.6.5.4.3.2.1 2 4 6 8 1 12 14 Figure 18: Potential measured when one junction is heated with a blowtorch and the other is in liquid nitrogen There is much more fluctuations in this format since the blowtorch does not provide a constant heat flow as would the liquid nitrogen or room air. However, the maximum potential obtained is 98.4 ±.5 mv, and the resistance in this case is reduced to.5 ±.1 Ω so the current is approximated as 196.8 ±.6 ma. Due to the large heat that the blowtorch provides to the junction, the aluminum rod broke apart and no more than 26 data points were available. None of these were really constant, but a large enough temperature without breaking the rod would be an effective way of obtaining a constant potential. 6 Acknowledgements We would like to acknowledge Professor Michael Hilke, and the T.A. s in the lab: Dick Creamer, Nazim Hussain (you da man!), and William Paul. And of course we must give an extra-big thanks to the real Lab Master, the lab technician, Mark Orchard-Webb. We thank them all for their help and patience, especially with these projects. References [1] OMEGA Complete Temperature Measurement Handbook and Encyclopedia, OMEGA Engineering, Inc., 1995, vol. 29 [2] Roberts, R.B. (1977), Absolute scale of thermoelectricity, Nature, 265: 226 7 [3] DiSalvo, F.J. (1999), Thermoelectric Cooling and Power Generation, Science, 285: 73-6 [4] Rockwood, A.L. (1984), Relationship of thermoelectricity to electronic entropy, Phys. Rev. A, 3: 2843 4 5 Conclusions The main results obtained in part 1 show a strong correlation to the Seebeck effect, although the polynomial associated with it is not found because of an unfortunate short-circuit. The results from this section would also have helped to characterize the calculation of the Peltier coefficients, although the 8